Solve for $k$, $ -\dfrac{5k + 7}{4k - 12} = \dfrac{10}{k - 3} + \dfrac{9}{k - 3} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $4k - 12$ $k - 3$ and $k - 3$ The common denominator is $4k - 12$ The denominator of the first term is already $4k - 12$ , so we don't need to change it. To get $4k - 12$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ \dfrac{10}{k - 3} \times \dfrac{4}{4} = \dfrac{40}{4k - 12} $ To get $4k - 12$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ \dfrac{9}{k - 3} \times \dfrac{4}{4} = \dfrac{36}{4k - 12} $ This give us: $ -\dfrac{5k + 7}{4k - 12} = \dfrac{40}{4k - 12} + \dfrac{36}{4k - 12} $ If we multiply both sides of the equation by $4k - 12$ , we get: $ -5k - 7 = 40 + 36$ $ -5k - 7 = 76$ $ -5k = 83 $ $ k = -\dfrac{83}{5}$